Actually, this would correspond to a fiberglass structure that is about 1.5 inches thick, on average.
A 100 foot tall hat, 54 feet in diameter is pretty massive.
Now if you want to argue that it is steel, first of all it would probably be rusty by now. Secondly, steel is about 5 times more dense than fiberglass, meaning it would be 1/5 as thick. That would translate to 1/3 inch thick steel plate, pretty impossible to form into the hat shape and more for battleship construction.
Finally, at each level they use a replicating curved shape. That means one mold for many pieces. That's how they can make it cost effectively. There is one mold for the brim, 5 for the 5 levels in the hat, and one for the round cap on the top. The entire skin would have been constructed from 8 molds, with fiberglas/polyester blown into them.
There are a total of 127 panels (I think), each with an average weight of 425 pounds. Pretty reasonable (the weight of two hefty guys per panel).
So I stand by my conjecture that the BAH is fiberglass.